| Program / Major | mDP | Goals |
|---|---|---|
| Mathematical Sciences Course | DP-4・2 | キャリアを見据えた高度な専門知識 現象の背後にある数理構造やデータのパターンを理論的に解析し、社会や自然科学、工学における複雑な課題に対して数理的視点から解決戦略を提案できる。 |
This class is a continuation of Numerical Analysis 1. The purpose of this class is to study various numerical methods for
interpolation, eigenvalue problems, matrix factorizations, least-squares problems, and systems of linear equations, focusing
on their underlying principles and the derivation of algorithms, and to develop the ability to perform appropriate numerical
computations and to evaluate the results correctly.
Numerical analysis and numerical algorithms, which form the foundation of numerical simulation, have become indispensable
technologies in modern research and development in tandem with recent advances in computing environments. Computer performance
has improved dramatically, and a wide variety of sophisticated tools are now available, providing an environment in which
simulations can be carried out with ease. However, any tool, if used without sufficient understanding of its underlying principles,
may sometimes be misapplied and lead to serious errors.
In this course, students will study various numerical methods for interpolation, eigenvalue problems, matrix factorizations, least-squares problems, and systems of linear equations.
The course will primarily consist of lectures, but students will also implement algorithms and conduct numerical experiments using computers. In addition to lectures, students will write actual programs and perform numerical experiments.
In this course, students will study various numerical methods for interpolation, eigenvalue problems, matrix factorizations, least-squares problems, and systems of linear equations.
The course will primarily consist of lectures, but students will also implement algorithms and conduct numerical experiments using computers. In addition to lectures, students will write actual programs and perform numerical experiments.
- Understand the working principle, implement the interpolation method and perform interpolation for given data.
- Understand the derivation and operating principles of algorithms for eigenvalue problems, and be able to compute eigenvalues in practice.
- Understand the derivation of numerical methods for solving least squares problems and be able to solve them.
- Understand the principle of operation of the conjugate gradient method and be able to calculate approximate solutions on a computer.
| final exam | reports and assignments | Total. | |
|---|---|---|---|
| 1. | 15% | 10% | 25% |
| 2. | 15% | 10% | 25% |
| 3. | 15% | 10% | 25% |
| 4. | 15% | 10% | 25% |
| Total. | 60% | 40% | - |
Final examination (60%), reports and assignments (40%)
Students will be considered to have passed if they are judged to have achieved approximately 60% proficiency in understanding the derivation and algorithms of each numerical method, implementing them on a computer, conducting numerical experiments, and appropriately evaluating the obtained results.
Students will be considered to have passed if they are judged to have achieved approximately 60% proficiency in understanding the derivation and algorithms of each numerical method, implementing them on a computer, conducting numerical experiments, and appropriately evaluating the obtained results.
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | Guidance Interpolation Method 1: Lagrangian interpolation |
Review of Numerical Analysis I | 190minutes |
| 2. | Interpolation Method 2: Newton Interpolation | Review of previous classes | 190minutes |
| 3. | Interpolation Method 3: PC Exercise | Review of previous classes | 190minutes |
| 4. | Interpolation Method 4: Spline Interpolation (1) | Review of previous classes | 190minutes |
| 5. | Interpolation Method 5: Spline Interpolation (2) | Review of previous classes | 190minutes |
| 6. | Interpolation Method 6: PC Exercise | Review of previous classes | 190minutes |
| 7. | Eigenvalue problem: Power method | Review of previous classes | 190minutes |
| 8. | Matrix factorization 1: Cholesky decomposition and its application to eigenvalue problems | Review of previous classes | 190minutes |
| 9. | Matrix factorization 2: QR decomposition and its application to eigenvalue problems | Review of previous classes | 190minutes |
| 10. | Least squares problem: Normal equations | Review of previous classes | 190minutes |
| 11. | Least squares problem: A method using matrix factorization | Review of previous classes | 190minutes |
| 12. | Conjugate gradient method 1: Minimizing residuals | Review of previous classes | 190minutes |
| 13. | Conjugate gradient method 2: Krylov subspace | Review of previous classes | 190minutes |
| 14. | Review and final exam | Review of previous classes | 190minutes |
| Total. | - | - | 2660minutes |
| ways of feedback | specific contents about "Other" |
|---|---|
| Feedback in the class |
Textbooks will not be specified; materials will be distributed as needed.
- Office Hours: Tuesday, 4th Period
If you have any questions, it is preferable to make an appointment in advance by email.
- Course that cultivates an ability for utilizing knowledge
- Course that cultivates a basic problem-solving skills
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A | 該当しない |
Last modified : Mon Mar 23 04:07:16 JST 2026